History shows that the Jews started moving out of the Middle East in the 1000s? Until then there were no major Jewish centers outside the Middle East (Babylon, Egypt, etc.) except for Rome. By the 1100's, most Jewish activity took place in Western Europe. What factors contributed to this transition?

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Jews had traditionally been a wide-ranging people. They had centers in Europe, Asia Minor, and even India. (When Thomas went to India in 52 AD, for example, he did so in part because there was already a thriving Jewish community.)

Starting in the 50s and 60s AD, many Jews were already being run out of the Israel (think Masada and all that). In 125 AD, Jerusalem itself was emptied of all its Jews, and dispersed throughout the Empire. Many ventured even further.

It isn't so much that Judiasm moved to Europe in the 11th Century, as the fact that the more learned and influential Jews were the ones that had moved abroad. As the various regions in which Jews had established a hold waxed and waned, so too did Jews in those regions. What you're identifying in European Judaism in the 11th Century is the emergence not of Judaism in that area, but rather of Europe itself.

Major incentives for the disperal of Jews out of Judaea were Roman campaigns, especially the Jewish war of the 60s-80s AD (led on the Roman side by Vespasian and his son Titus) that culminated in the destruction of the Jerusalem temple and the end of the so-called 'temple Judaism' as opposed to 'Rabbinical Judaism', based not on one cult center but rather on the teachings and scripture. Another blow was dealt by the emperor Hadrian, who prohibited circumsision and renamed Jerusalem Colonia Aelia Capitolina; to this day, Hadrian's name is invoked in Jewish context with a spell meant 'let his bones be crushed'.